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base morality

A while back a muslim redditor asked a novel question, which i suspect lies toward the heart of many people’s attachment to religion in a (comparably) secular society, especially as a source and framework for morality:

So a lot my atheist friends tell me that I am “nitpicking” the good parts of Islam and the Quran and ignoring all the bad stuff that it preaches. I completely agree with them, I do that all the time. Ive just wondered why that is considered bad. I understand that if I dont follow all of the rules, Im not really 100% muslim, but thats okay with me. Im only like 75% muslim. I only believe in the part of the religion that I want to, but I think I believe in enough to still call myself a follower. Is that wrong?

This gave me the chance to expound upon a perspective on scriptural morality i’d been nursing for some time, and my response was well-enough liked that i suppose it’s worth expanding upon here.

First, of course, OP meant cherry-picking, which refers to biased (though not necessarily conscious) selectivity in sourcing—for instance, citing only studies that (can be twisted to) support your point of view, or adhering only to scripture that agrees with your personal moral framework, or even acknowledging only those components of a contrary argument to which you have a ready-tailored rebuttal—not nitpicking, which, as i and several other people who made this clarification pointed out, we were engaged in.

Now, easing into the question itself, there are several obvious (and other subtle) problems with reducing one’s adherence to a religion to a percentage. The demarcation of religious belief is itself fuzzy, fluid, and inconsistent; and even were the various parameters projected onto some unidimensional scale there would arise serious objections to expressing the location on this scale statistically as a percentage—percentile, perhaps, were one to be sorted among the population of self-identified adherents, but percentage carries categorical as well as representational implications.

Ignoring this, it’s intuitive, if not transparent, what someone means when they identify as “75% muslim”. So let’s assume this intuitive meaning. In my opinion, OP’s explanation succumbs to something akin to the base rate fallacy. In fact, i will argue that an appropriate rigorous rendering of this statement, in probabilistic terms, commits precisely this fallacy. First let us build upon the original intuition.

Consider a simplistic analogy. Pretend that the Protestant Ten Commandments constitute the entirety of Protestantism. That is, adherence to Protestantism consists of adherence to the following edicts (somewhat charitably paraphrased):

  1. Have no other gods before Yhwh.
  2. Neither create nor worship likenesses of nonhuman domains, under penalty of generational disfavor.
  3. Take not Yhwh’s name in vain.
  4. Labor only six days in seven, and ensure that your property does the same.
  5. Honor your parents, under reward of longevity.
  6. Commit no murder.
  7. Commit no adultery.
  8. Commit no theft.
  9. Bear  no false witness against your neighbor.
  10. Covet no property of your neighbor.

We might then call someone “N * 10% Protestant” if they follow N of the commandments strictly but completely ignore the others, or more generally if they follow the commandments at varying rates that sum to N.

There are a couple of shortcomings in this translation from intuition to percentage. One is that the percentage description fails to account for any existing moral codes, which may overlap with the commandments, already followed by most of the population regardless of religious affiliation. For instance, a typical secular humanist would follow Commandments 5, 6, 7, 8, and 9 fairly closely (allowing room for flexibility in nuanced situations), these being variations on common decency, despite having strong objections to the remainder, which essentially constitute appeals to piety and an admonition against thoughtcrime. Would such a secular humanist consider themselves 50% Protestant? Reciprocally—and perhaps more relevantly—would a typical Protestant consider this secular humanist 50% Protestant? Surely not.

Instead, the commandments that count toward someone’s Protestantness (Protestanticity? Protestance?) should be those—and only those—that set Protestantism apart from the morality of the ambient culture, i.e. those edicts followed by most people most of the time, and agreed upon by nearly everyone. (In my reply i referred to these as “secular morals”, a clumsy choice; secular—meaning, religiously indifferent—morality leads to many prescriptions that receive majority opposition, and certainly do not constitute a cultural ambiance.) Whereas honoring one’s biological parents is not so widely-shared a virtue as Protestants might wish (nor is this necessarily a bad thing), Protestantism might be partially credited for someone adhering to this edict; but no credit would be due for an abstention from (illicit) adultery, because this is almost universally understood to be moral (if likewise far from universally practiced).

Along the same lines, the credit dealt our simplistic approximation to Protestantism for this decalogue would better be balanced not against an isonumeral secular alternative but against the full range of moral tenets a person might, if presented therewith, adopt into their worldview. If our secular humanist above also happens to abstain from animal cruelty, torture, bigotry, and plagiarism, then they are clearly less Protestant for it, being that they have enriched their worldview far beyond the implications of these commandments. Should even a self-identified Protestant similarly abstain from such acts on moral grounds, is it not fair to describe them, having distanced themselves from Protestantism by dilution rather than by omission, and thereby transcended the decalogue if not transgressed upon it, as less Protestant?

This sets aside any conflict between the morality adopted from without a religion and that within. Religious tolerance, for example, is a virtue OP espoused that not only could not have been derived from primary sources but very likely runs afoul of them.

The question that arises out of these considerations is how to quantify the role a religion plays in one’s life, while being fair to the other sources upon which one draws in the construction of one’s worldview. A rigorous, and necessarily tedious, rendition might look like this:


Take the collection TR of proclamations, prescriptions, and other agreeable or disagreeable tenets of a religion R. If you wish, assign a weight to each tenet by its importance (otherwise assuming equal weight). Consider drawing a tenet at random from TR, a higher-weight tenet being the more likely to be drawn, and let P(A) be the probability that you agree with the tenet. Rigorously stated, OP suggests that you are p * 100% muslim if P(A) = p.

This statement requires a mathematical formulation of the context discussed in the preceding paragraphs. The latter consideration was the collection of all tenets that might factor into a person’s worldview. This is known in probability as the sample space. The weights of the tenets imbue the space with a categorical probability distribution. Of concomitant importance is how (let’s just say whether) agreeable you (would) find each of them. The probability P(A) that you would find a randomly selected tenet agreeable is then the base rate.

While there may be among these tenets commandments and countermandments on issues that bear so little relevance to your life that neither is particularly agreeable (whether or not to step through a door with your right leg, for instance; or, for another instance, Commandment 10 above), let us attribute to these such minuscule weight that we may consider the full gamut of tenets approximately balanced between agreeable and disagreeable. That is to say, let us assume for the purpose of illustration that the base rate is .5.

We have reframed the question, so we must adjust notation accordingly: p refers to the probability that you will find a randomly chosen tenet agreeable provided the tenet is drawn from religion R.* Formally, this can be written p = P(A|R). Whereas this answers the question “How agreeable is R to you?”, it fails to answer what i contend is a more faithful phrasing of OP’s question, “How well does R inform your worldview?” This question would better be formalized as follows: Should someone draw a tenet at random from your worldview, what is the probability that this tenet may be found in R?

Now we come to my charge. The base rate fallacy, the fallacy of inferring the answer to the latter question from that to the former, can be formalized like this: P(R|A) = P(A|R). This is mathematically equivalent to the common mistake of inferring, from a clinical trial that reports a statistically significant effect at the .05 level, that the effect is at least 95% likely to be real. The base rate fallacy is often called the “p-value fallacy” for this reason.**

To calculate P(R|A), we may take advantage of Bayes’ Theorem:

P(R|A) = P(A|R) * P(R) / P(A)

We have named P(A|R) = p and provisionally settled upon P(A) = .5, but we do not yet have a handle upon P(R), the probability that a tenet chosen randomly from among the plethora of tenets available to us happens to be found within religion R. There is of course an infinitude of possible proclamations, prescriptions, and so on that might be proposed, but let us assume that they are of vanishing importance as they become more complex and provincial. While many of those found within any mainstream religion’s scriptures would certainly join these vanishing ranks, the more celebrated may be attributed some non-negligible proportion q. That is, suppose that the tenets of religion R, weighted by importance, constitute q * 100% of the weighted sum of all tenets by which people might live, so that the probability of a randomly chosen tenet being found in R is P(R) = q.

Now, i would assert that, even among the most universally celebrated of scriptural pronouncements, there remains a deplorable absence of vitally important tenets, especially for a text that purports to be a definitive (or at least definitional) guide to human knowledge and morality. The Bible, as many point out, includes precious few admonitions against the most costly atrocities of the past several millennia, including genocide, slavery, oppression, and ecological despoilment, and while one might argue that these are implied by simpler decrees like those encapsulated in the decalogue, the recurring scriptural endorsements of such programs as the aforementioned call this inference into question. I suspect that other holy texts are not substantially different in this regard.

To be somewhat generous, therefore, we might set q = .01; however, to preserve whatever devout readers might still be reading (and implicitly and rather presumptuously to assume that any began in the first place), we might instead set q = .1 and declare that we are compromising preemptively with the oft-asserted claim of q = 1 by way of a geometric average. (This is probabilistically meaningless but emotionally satisfying. The beauty of this entire approach is that one may experiment across a range of values of q to figure out (retrodict) just how weighty a religion must be in order for the maths to play out in the apologist’s favor.) Note that we are attributing to R at best a fifth of (the weight of) all possible agreeable tenets, since we have taken its weight in proportion to all to be one tenth, and at worst a fifth of all disagreeable tenets.

Using P(A|R) = p, P(R) = q = .1, and P(A) = .5, we therefore have

P(R|A) = p * .1 / .5 = .2p.

That is, whatever proportion of tenets of R you find agreeable, that times 20% is the extent to which R informs your worldview—put more carefully, p * 20% of your worldview could be explained by your adherence to R. Taking R to be Islam and p to be OP’s asserted p = 75%, this leaves OP justified (again, in my view) in attributing 15% of their worldview to Islam. Not quite so impressive, is it?


The problem is confounded by the overlap in prescriptions across religions. If, for instance, if we reduce Buddhism to these five tenets, then by OP’s criteria any strict Protestant is already at least 60% Buddhist. Taking tenets in full, the Abrahamic religions very probably overlap in the majority of their proclamations and prescriptions. This might be accounted for mathematically using an inclusion–exclusion model, but the complexities and vaguenesses of the canonical texts might make such an approach intractable.

The above pedantry and rigor allows us to at least be consistent in how we quantify our affiliations. Even this, however, is a dubious quantification, and for its inconsistency with other aspects of our identities may even be intellectually dishonest.

For the most part, we do not affiliate with religions because we each independently discover their texts and find ourselves in unexpectedly broad agreement, any more than we assume hundreds or thousands of other labels as we happen across mythological, fictional, philosophical, and scientific literature that resonates with and informs our beliefs. We affiliate with religions because they occupy a privileged status in our literature and heritage arising largely (entirely?) out of their perpetuity. Like surnames, their absence is more conspicuous than their presence. Even if we are not indoctrinated from childhood, so long as we are unaffiliated we are regularly made conscious of it. This custom is on the decline but remains in effect.

The upshot is that we are not poised to defend our religious faith—or, rather, affiliation—on probabilistic grounds, even if we perceived some reason for us to do so. A challenge to faith on these grounds would be as meaningless as a defense.

One last phenomenon i find worth commenting on is the apparent novelty with which many religious and irreligious people are primed to view secular morality. It has become such a trope that our moral codes are grounded in religious scripture that people with no particular religious affiliation will take to calling themselves “good Christians” or receiving this branding as a compliment, or interpreting frameworks for secular morality as religions of their own. We may even cite the absence of a moral foundation as a fundamental problem with secular government!

In contrast, i assert that this (often very consciously perpetuated) conflation of religion with morality undermines morality, as—like literature and sports—an evolving and cumulative human enterprise, and moreover as—like science—one that undergoes revision and refinement as present limitations are pushed, new avenues are explored, arbitrary features are dismissed, and blind alleys are abandoned. At any of these points is scriptural morality primed to inhibit the endeavor, by imposing arbitrary boundaries or introducing artificial controversies.

No less sinister, in my view, are the implications at the personal level. Limiting our moral framework to the edicts of scripture inhibits our growth and maturity as moral agents; and attributing what morality we do embrace, or even develop on our own, to a religion absolves us of the responsibility for questioning, revising, and honing it. (I challenge anyone to spend a moment’s thought but fail to conjure a contemporary example of either of these.) These charges might be better situated within an essay extolling the virtues and promise of secular morality, but in the meantime it will suffice to have them highlight the misguidedness of the entire preceding discussion—however fun a word problem it might make.

* We implicitly assume here that the weights of tenets within R are in proportion to their weights without.

** It is also, it seems to me, the root of such nonsense phrases as the following from a neighbor of mine, appended—as though to raise the shock value—to a newspaper account of a family so desperate that sold their child into slavery: “And these were probably Christians!”

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  1. February 8, 2013 at 11:07 pm

    Quick question: do you think that adhering to certain instructions within a religion/ideology and discarding others, but still referring to oneself as a member of the group in question is inherently hypocritical? In other words, is a worldview defined by the instructions it’s authors left for their followers, or by the way in which it’s authors & followers perceive the world?

    • February 10, 2013 at 12:53 am

      You have called me out. :) I think a great deal more than the correctness of truth claims is worth considering when we adopt identities and affiliations. Atheism+, for instance, is probably no more true in the broad agreements among its affiliates than humanism (or Humanism), and Occupy Wall Street arguably less so than the Democratic Party. I adopt these affiliations because the issues speak to my emphases as well as to my beliefs, or rather speak to my beliefs in better proportion, and i get the strong impression that this holds true for many religious folk as well. There’s nothing wrong with that.

      The caveat is that affiliations come with responsibility. To some non-negligible extent, every self-identified Democrat (registered or not) is complicit in the criminal negligence of the party toward such issues as climate change and prison reform, as every self-identified Christian is likewise (to some extent) complicit in the Catholic Church’s crimes against humanity—in part because that implicit demographic support bolsters their clout, in part because appropriation (of a dominant label) itself constitutes a form of protective shielding. Some labels are, i think, unsalvageable. (There’s essentially no excuse to identify as a Republican.) But others i don’t mind people identifying with provided they recognize their responsibility to atone for the cost on others than themselves of the impact of that label (i.e. organization, worldview, etc.). I’ve got a half-written post on the backburner on this point that i should probably just suck up and finish; stay tuned, and thanks for the prompt.

      • February 10, 2013 at 1:04 am

        Glad to help. I appreciate the response; this is a question I’m working through myself.

  2. November 30, 2012 at 4:00 pm

    There may be another way to statistically analyse the question raised here. One of the things that we often worry about philosophy of science are questions about when we can say that we favor one hypothesis over another. One thought on how to do this is to use the so-called “Likelihood Principle”:

    Given some evidence e, hypothesis h1 should be preferred over hypothesis h2 if P(e|h1)>P(e|h2).

    It turns out that this principle can be derived from Bayes’ Theorem (and is central to my present research).

    Here, it seems like the OP might ask whether we should favor the hypothesis that s\he is a Muslim over the hypothesis that s\he is not a Muslim:

    Is P(e|Muslim)>P(e|~Muslim)?

    In other words, is it more likely that OP is a Muslim than not? [We refer to P(e|h) as the likelihood of h given the evidence e.]

    • December 7, 2012 at 3:48 am

      Hi Dan! Thanks for commenting, and please continue if you’ve a mind to.

      I probably should have mentioned the likelihood principle at the outset, since in some sense i am making a case against it—or, at least, for an improvement upon it. I might end up talking past you (i.e. missing your point), but, just in case, and for the benefit of anyone reading, here we go.

      Essentially, my argument is that how well Islam describes one is a better interpretation of “how likely it is that someone is muslim”, or “how muslim someone is”, than how much of Islam one ascribes to—and then that, while P(e|Muslim) easily quantifies the latter, P(Muslim|e) better quantifies the former. (I should note again that i am not talking about personal identity, but rather about adherence to a predefined religion.)

      Notice that, since P(e|Muslim)P(Muslim)+P(e|~Muslim)(1–P(Muslim))=1, the inequality you describe is equivalent to P(e|Muslim)>P(e), which by Bayes’ Theorem is equivalent to P(Muslim|e)>P(Muslim). We are only talking about the effect of the evidence here; the base rate fallacy is not an issue. Any concordance between Islam and OP’s worldview strengthens the claim that the former informs the latter.

      Hidden from this analysis, though, is whether this evidence would be enough to tip the balance from “insufficient reason to credit Islam” to “sufficient reason to credit Islam”. That requires knowledge of the existing reason P(Muslim) we already had, plus knowledge of the “power” P(e) of the test that produced the evidence.

      If i continue any further then i’ll just end up rehashing things already much better said by others. For a full discussion of how these factors play out, see in particular David Weinberg’s illustrative post “The Plausibility Problem”.

      Note: Sorry for all the onosecond edits.

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